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Erik, I presume what you call the Monty Hall problem is in summary this:

You’re in a game and you have to choose one of three doors behind which there may be a prize (apparently in this case a donkey, hmm, maybe not a prize then ;-)

After you have chosen a door, the game show host opens one of the other doors behind which there is no prize.

You get the chance to change your choice of doors.

The correct answer is that you should switch your choice without thinking, because it doubles your chance to get the prize. Is this the problem we are talking about?

Most people will intuitively feel that there is now a new situation where you have a 50% chance of getting the prize, because there are two doors left and one of them has the prize.

The reason this is not the case is in rule number 2 above. The important part is that the host chooses one of the other doors and never the door you have chosen. Now, this gives you two possibilities:

You initially chose a door with the prize: (33% chance) -> This is easy for the game show host, he can chose any of the other doors. The other door has 0% chance to contain the prize. Switching will give you the wrong door.

You initially chose a door with no prize (66% chance) -> The game show host has no choice. He has to choose the remaining empty door. Now this is interesting. The other door has 100% chance of containing the prize. Switching will give you the right door.

See, because the chance to choose a room with no prize initially is twice as high, you have a bigger chance that the game show host is forced to open the other empty room, which gives a bigger chance for the third room to contain the prize.

Does that help? Or were you talking about something else entirely? ;-)

Update:

Maybe this is a better summary:

If you choose right the first time, switching will never give you the prize. If you choose wrong the first time, switching will always give you the prize. There’s a much bigger chance you choose wrong (2 out of 3).

Perhaps a real mathematician can help me here. I just don’t understand the supposed solution to the Monty Hall problem.

I understand the reasons that it is supposed “unintuitive” but I still believe them. Allow me to forumlate the objection in a way that seems novel.

Once Monty reveals the Donkey, and you are given what is in reality a new problem – pick a door with a 50% probablity of any one being the right one. The thing is that switching from your originally selected door doesn’t change the probability of the door being the right one. Merely the act of revealing the donkey behind one of the unselected doors does.

So what’s critical is selecting a door under these new odds – which is exactly what Monty is letting you door. The key for me is that even choosing to keep the door you already have is a selection.

Here is what’s cool about this blog post – I’m doing it all with flock.

I think I may do a little review of this new still pre alpha browser. When I first heard of it I was very dubious about it. But after only five minutes of use, I “get” it. Flock may not be the browser for me, even when completed, but I understand the Flock philosophy now, and understand why it’s developers seem so excited.

At heart, Flock seems to be gunning for making the read/write web we were all so excited about 10 years ago but didn’t get. It’s tactic is that sites like del.icio.us and tools like weblogs are effectively adding the write/share features of the old Web vision on top of the current read/display web that we’ve got – so why not make a browser that combines all those things transparently. For example, when I say that I’m blogging this with Flock, I don’t mean that I surfed to the WordPress login with Flock, I mean that I used Flocks built in blogging tool to write this blog – Flock autodetected how to connect to the XML-RPC service that WordPress provides, and is making this post for me. All I needed to do point it at blog.xfce.org and enter my information.

I myself am not ignorant in the ways of public manipulation. This is a win – win for Thompson. If the game isn’t made, then he spins this as reveling the hypocrisy of the video game industry. Blithely ignoring that studios exist to make money, and producing a game that is directly insulting to their target market is tantamount to suicide, Thompson will claim that the absence of his game points to a hypocrisy in the industry. Underneath, Thompson will say, they know that such a game would cause a flowering of violence in the real world.

And if the game is made? Thompson has created a scenario so horrific that the studio who made it will have made only more evidence for Thompson’s claim that we are all depraved, vicious peddlers of filth and darkness to the fragile and pure children of America.

Thompson misses the essential truth – that America is a disgustingly violent place. The fragile and pure children are nowhere to be found. We live in a culture of violence, in a time of unjustifiable military action, in land stolen from it’s native people by application of force, whose media from Saturday morning cartoons to the evening news is saturated by blood. One wonders if perhaps Thompson himself carried violence in his heart – is this scenario of his what his dreaming self wants to do to the video game industry? When Jack Thompson writes the name “Osaki Kim” does he breath the words “Jack Thompson?”

More to the point, does old Jacky boy not realize that he has created the perfect opportunity to satirize himself, and display as only interactive fiction can, his own lunacy? Showing, in grim high def 3-D detail, the senseless murder of pale, scrawny, geeky high school aged video gamers, innocent and defenseless, by a man who has been told by his culture to take retribution out of the hands of the court and into his own will not help make Thompson’s case.

Thompson is saying very little new – writers, filmmakers, musicians, all have been blamed in the past for our cultural degeneracy. What Thompson adds to the mix is his subtle finger pointing at us, the gamers. Saying that it is our weakness of character, our support for video games that is the real cause of rape and murder – effectively, Thompson is blaming me and mine. Thompson still lives in a world where gamers are the minority, and can be blamed for those things which are epidemic to this country. And that is so insulting, and so irresponsible, that I believe Thompson’s charge must be taken up.

Games can contain stories, and stories can contain ideas. All Thompson sees is gore and robots, just as all my grandparents heard in the Beatles was sex and drugs. He cannot see the ideas, and as a man with no soul he cannot see the power of storytelling. He has presented us with a scenario which a talented game designer could turn into a bleak tale of individual madness, the culture that praises and nurtures it, and the idiocy of the scapegoat.

I truly hope that someone with the talent and the balls takes up the task.